Did my dentist mean to cut the gum of the tooth beside my temporary crown?

During tooth preparation and impressions of the tooth prep, the gums may need to be retracted, especially if the crown is prepped below the gumline. The tissue around the crown prep may be tender and slightly swollen for a few days after your appointment. For some relief, you can do warm saline rinses, and be sure to brush and floss regularly to keep the area clean. I hope this helps.  Follow me for more questions and answers.

Most likely your dentist packed the gums to allow good visibility of the tooth. This will allow a better fitting crown. Ask your dentist if he/she knows of a product called Oxygel. This product has a very active form of aloe which is very soothing and healing to the gums. Look for Oxyfresh dental gel online (I have no commercial interest in this product).

I have used it for years with great results. If you are allergic to mint don't use it. It will usually take 7-10 days for the gums to heal. Be patient and you will have a great result.

Without a picture it's difficult to answer your question . Please post a picture if you would like a response. 

Depending on how far under the gum your crown goes, sometimes the gum has to be adjusted in order to capture the tooth properly during the molding. Typically, the gum tissue fills back in without any issue. Over the next few days you will see that improve. Keep the area clean by brushing and flossing.